(Solved): 5. Assume that the graph below is the graph of the derivative f(x) of a function f(x). (a) Deter ...

5. Assume that the graph below is the graph of the derivative $$f^{?}(x)$$ of a function $$f(x)$$. (a) Determine the intervals where the function $$f(x)$$ is increasing/decreasing. (b) Determine the intervals where $$f(x)$$ is concave up/down. (c) Using parts (a) and (b), determine whether the function $$f$$ is increasing or decreasing and whether it is concave up or down at $$x=?1$$. (d) Do the part (c) for $$x=?4$$. Extra Credit. Determine the values of the coefficients $$a,b,c$$, and $$d$$ so that the cubic function $$f(x)=a{x}^3+b{x}^2+cx+d$$ has a local maximum of 7 at -1 and a local minimum of -20 at 2 .